Stability of synchronized distributed control of discrete swarm structures

Investigates the stability of synchronized distributed control of 1D and 2D swarm structures. A new distributed control method for swarm structures is proposed. The dynamic range of swarm structures under synchronized distributed control is discussed. The authors prove that both 1D and 2D swarm structures are stable with appropriate weights in the sum of adjacent errors if the vertical disturbances vary sufficiently more slowly than the response time of the servo systems of the agents. It is also proven that the Lyapunov functions of swarm structures are monotonically decreasing, and tend to zero as the time goes to infinity; hence there is no local minimum